The invention relates to torsional vibration damping apparatus in general, and more particularly to improvements in torsional vibration damping apparatus which can be used with advantage in power trains between the engines and variable-speed transmissions of motor vehicles. Torsional vibration damping apparatus of the type to which the present invention pertains can be embodied in or can constitute clutch plates (also called clutch discs) for use in friction clutches of motor vehicles Reference may be had, for example, to French Pat. No. 2 551 813.